No, the graph tracks all deaths. Which is apparent both from the labeling (read it closely) and the fact it is tracking deaths from long before Covid-19 was a thing.
Some of them would have died of other causes, but not that many and not this quickly.
Furthermore, Covid-19’s disruptions to healthcare mean that others are dying due to the impact of the disease despite not being infected themselves. Nobody knows exactly how many, but it exceeds the 280,000 Covid deaths (current figure) generally reported in the media. Probably by 50,000-100,000.
So yes, looking at excess deaths gives a better sense of Covid-19’s total impact on public health but it also paints an even worse picture.